In the state of the art, rolling stands for strip or sheet, particularly four-high stands, use techniques with an axial movement of the rolling rolls.
These techniques serve to ensure a better control of the planarity and profile of the strip and to distribute wear uniformly over the surface of the rolls, particularly to prevent the edges of the strip from acting always in the same zones of the roll surface.
Therefore, in the state of the art, at least the working rolls are subjected to axial translation (shifting) to vary the surface of the roll subjected to the rolling load, so as not to cause areas of most likely wear on the surface of the rolls.
These techniques, adopted for rolls with a plane surface, are widely used and have been thoroughly explored in many applications.
The state of the art also includes rolling rolls with profiles shaped so as to ensure a more precise control of the profile of the strip by means of simple and reliable systems to move the rolls.
To this end there have been proposals for shaped profiles, described by quadratic, cubic, fifth order or polynomial equations in general, which allow to configure a precise control of the strip analytically, defining a specific shifting program, thus obtaining profiles characterized by a desired development more or less rounded.
However, if we use rolls with a surface described by a polynomial curve and where the shifting of the upper roll is the same as and of the opposite sign to that of the lower roll, there is the serious disadvantage that, to obtain a particular profile of the strip, the working rolls must always be in fixed and pre-determined positions.
For example, let us consider the case of working rolls whose profile has an anti-symmetrical cubic development (FIG. 1) which can be described by the equations: y.sub.1 (x)=ax.sup.3 +bx+t.sub.h and y.sub.2 (x)=ax.sup.3 +bx respectively for the upper roll and for the lower roll, where t.sub.h represents the value of the gap between the rolls when in a stationary condition.
When the shifting condition is nil, and the median axes of the rolls are substantially aligned, the value of the gap is constant: t(x)=const=t.sub.h.
If the two rolls are offset with respect to each other at the outset, respectively one by the quantity (x.sub.0) and the other by the quantity (-x.sub.0), the gap function, in a shifting condition of nil, is defined by the equation: t(x)=y.sub.g1 (x)-y.sub.g2 (x).
Since y.sub.g1 (x)=y.sub.1 (x+x.sub.0)=a(x+x.sub.0).sup.3 +b(x-x.sub.0)+t.sub.h and y.sub.g2 (x)=y.sub.2 (x-x.sub.0)=a(x-x.sub.0).sup.3 +b(x-x.sub.0), developing the powers and carrying out the calculations we get the equation: EQU t(x)=6ax.sub.0 x.sup.2 +2ax.sub.0.sup.3 +2bx.sub.0 +t.sub.h =.alpha.x.sup.2 +.beta. (1)
from which it follows that the profile of the gap between two rolls whose profile is described with an anti-symmetrical cubic curve, in conditions where the rolls are initially offset, has a parabolic development.
If we now consider applying a symmetrical shifting to the working rolls, for example of an entity "+s" for the upper roll and "-s" for the lower roll, we have the gap described by the following parabolic equation: EQU t(x)=(6as)x.sup.2 +(2as.sup.3 +2bs+t.sub.h) (2)
For a strip or sheet of a width 2w, the crown, defined as the difference between the gap value in correspondence with the center line of the strip, gap (0), and the value in correspondence with the edge of the strip, gap(w), is thus equal to: t(x)-t(0)=6asw.sup.2.
Therefore, for positive shifting values (s&gt;0), the crown will have a convex development (FIG. 2a), while for negative shifting values (s&lt;0), the crown will have a concave development (FIG. 2b).
Shifting applied to the working rolls in any case causes the gap value to vary in correspondence with the center line: EQU gap(x=0)=2bs+2as.sup.3 +t.sub.h
So as not to modify the value of the gap, it is therefore necessary to reposition the two rolls, one with respect to the other, by the quantity 2bs+2as.sup.3.
This operation is made by repositioning the hydraulic capsules or electromechanical screws which act on the chocks of the rolls by the same height, that is, a value equal to (2bs+2as.sup.3).
From the above, it is obvious how the control of the strip profile is completely rigid if symmetrical shifting of the working rolls is used, that is, if the rolls are translated in the opposite direction with respect to the center line by an equal value "s".
In fact, once a target crown value has been defined with the stand unloaded, that is to say, in a condition wherein no pre-determined bending is imparted to the rolls, it follows that to obtain this target crown value there is only one value of "s", that is, the one defined by the equation s=target crown/6aw.sup.2.
This leads to the disadvantage that, in the case where there is a shifting of the upper roll equal in absolute value and of the opposite sign with respect to that of the lower roll, to obtain a particular profile, characterized by a desired crown, the shifting value is univocally determined and with it the position of the working rolls.
This minimizes the benefits of making the wear on the rolls uniform, for which reason shifting is used in the first place.
In fact, by using a bending operation on the working rolls it is possible to obtain a target crown value, that is, a strip profile value, with wider shifting values, that is, there will be a shifting defined by a value "s+.DELTA..sub.1 " for one working roll and "-s-.DELTA..sub.1 " for the other working roll.
The amplitude of the field of variability caused by the shifting operation, and with it the possibility of preventing the edges of the strip from always affecting the same zones of the surface of the rolls, will therefore depend on the available bending value (positive and negative); the higher the bending available, the greater is the possibility of obtaining a target crown in a wide range of shifting values.
This allows to distribute the wear over a wider band of the surface of the rolls, the value of which depends on the value of .DELTA..sub.1.
Thus, even if using bending makes a rolling process using working rolls having a profile with a cubic or polynomial development more flexible, this in any case does not allow to satisfactorily prevent wear in correspondence with the edges of the strip.
Therefore in any case, especially in hot rolling mills and to obtain thin plane products of high quality, one is obliged to use rolling techniques which solve this problem of wear, for example by rolling strip of a progressively decreasing width to avoid repeated passes in the worn zones of the rolls.
This problem, which still has not been solved and which businessmen working in this field still complain of, considerably limits the possibility of using cubic profiles for working rolls and therefore constitutes a considerable constraint on the development of rolling techniques using rolls with shaped profiles.
The present Applicant has devised and embodied this invention to overcome this shortcoming and to obtain other advantages as explained hereafter.